Solved: Estimating infinite sums Estimate the value of the

Chapter 10, Problem 35E

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QUESTION:

35-38. Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than \(10^{-3}\).

\(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{k^{5}}\)

Questions & Answers

QUESTION:

35-38. Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than \(10^{-3}\).

\(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{k^{5}}\)

ANSWER:

Problem 35E


Estimating infinite sums
 

Estimate the value of the following convergent series with an absolute error less than 10-3.

Solution:

Step 1
For the given convergent series we take .

The given series is an alternating series and that

a. and decreasing monotonically.

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